Ten times in a dozen seasons, one team has held the title and received the accompanying playoff berth.

Since 2001, when New England’s run of divisional dominance began, other teams have had success in their divisions. The Colts have won seven of the 10 AFC South titles since NFL realignment in 2002. Pittsburgh has won six AFC Central/North titles. The Eagles have won the NFC East six times.

Fine achievements all, and certainly plenty to be proud of.

But 10 times in 12 years?

You start to wonder how one team could be so much better than the other three for such an extended period of time, and you quickly realize it boils down to two things: stability and an elite quarterback.

Having one or the other is fantastic. Having both can make a team great.

Look at the teams mentioned above as being strong in their division: Indianapolis had the same general manager, Bill Polian, and the same quarterback, Peyton Manning, for 14 years. One Super Bowl and two AFC championships later, the franchise and the duo parted ways.

Kevin Colbert has been the general manager of the Steelers since 2000, and the team has had the same starting quarterback, Ben Roethlisberger, since 2004. Pittsburgh has made three Super Bowl appearances in that time, with two wins, though it was done with two head coaches.

Philadelphia’s Andy Reid is likely in his last season with the team, but he has been with the Eagles since 1999, and that same year Donovan McNabb was drafted to be the franchise quarterback. They were together for five of those six NFC East titles, five NFC Championship games, and one Super Bowl.

The story is no different in New England. Bill Belichick arrived in 2000, and a year later a twist of fate led to Tom Brady becoming the starting quarterback three games into the season.

As they say, the rest is history.

Or misery, if you’re one of the other three teams in the AFC East.

At least the Jets (2002) and the Dolphins (2008) have been able to say that they were able to wrest the title from New England’s grasp in the last decade-plus. Buffalo hasn’t won the division since 1995.

It seems like such a simple equation: coaching/front office stability + quarterback = wins, but clearly it isn’t easy to solve, not for the three other AFC East teams — though they certainly aren’t alone.

Since Brady took over in 2001, only one other quarterback has started a game for the Patriots: Matt Cassel, who was forced into duty in 2008 when Brady suffered a torn ACL in the season opener.

In that same time span, the Jets have had seven quarterbacks start at least one game. In that same time span, the Bills have had eight quarterbacks start at least one game.

In that same time span, the Dolphins have had 16 quarterbacks start at least one game. Really, 16.

The most successful of those 31 QBs was Chad Pennington, who was the primary starter for the 2002, ’04, and ’06 Jets teams that went to the playoffs and also was the starter for Miami’s last postseason appearance in 2008.

Pennington, not surprisingly, is also the only one of those quarterbacks who put up a respectable touchdown-to-interception ratio during his time as a top signal-caller, one of the better indicators of success at the position.

Knowing who will be manning the most important position on the team week after week and season after season is a big plus, Belichick acknowledged.

“The ball runs through [the quarterback’s] hands on virtually every play, one way or another,” said Belichick. “What the player does well, what his strengths are, being able to build around them, whether it’s personnel or scheme.

“Likewise, things that that player doesn’t do well or maybe aren’t his strengths, working around those and not emphasizing those things but emphasizing something else.

“Each team, each player, has their own strengths and weaknesses, but if you can count on somebody being there on a consistent basis, then you can plan and work around that to a certain degree.

“Tom has a lot of strengths; he does a lot of things well, so there aren’t a lot of limiting factors with him. Really it opens a lot more doors than closes them.”

While New York has had three head coaches, Buffalo four (plus one interim), and Miami five (plus two interims) since 2001, the Patriots have had one head coach, who is also the primary decision-maker when it comes to personnel.

Stability + an elite quarterback has equaled a 142-45 regular-season record for New England since that first division-winning season of the Belichick-Brady pairing.

Instability + mostly below-average quarterback play has equaled a 94-93 mark for the Jets in that span, 86-101 for the Dolphins, and 72-115 for the Bills.

Ryan Tannehill, the Dolphins’ newest quarterback, called Sunday’s matchup against the Patriots “just another game.”

What the rookie apparently doesn’t realize is that until his franchise has that elusive stability, that unless first-year coach Joe Philbin is the coach it’s needed and unless it discovers that Tannehill indeed is the top-level quarterback it’s been searching so long for, Miami won’t have a chance of beating that “just another” opponent in New England.

Maybe it isn’t fair to compare the other franchises with New England. Robert Kraft was shrewd enough to take a chance on Belichick, whose first head coaching stint, with Cleveland, was memorable for the wrong reasons, and Belichick listened to Dick Rehbein when the late quarterbacks coach wanted to take the skinny kid from Michigan with the 199th pick in the 2000 draft.

In all of the years since, the other teams in the AFC East have been searching, mostly in vain, for that front office and coaching stability, for that quarterback who can raise the standard for his teammates and the entire organization.

Belichick and Brady wound up being a marriage made in football heaven, the once-in-a-generation matchup of the right coach with the right quarterback.

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